{
  "id": "1704.01928",
  "version": "v1",
  "published": "2017-04-06T16:48:57.000Z",
  "updated": "2017-04-06T16:48:57.000Z",
  "title": "Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes",
  "authors": [
    "Nicolas Champagnat",
    "Denis Villemonais"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka-Volterra birth and death processes and Feller diffusions with competitive Lotka-Volterra interaction. To this aim, we develop original non-linear Lyapunov criteria involving two Lyapunov functions, which apply to general Markov processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-06T16:48:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "37A25",
      "60B10",
      "92D25",
      "92D40"
    ],
    "keywords": [
      "absorbed markov processes",
      "uniform convergence",
      "conditional distributions",
      "original non-linear lyapunov criteria",
      "general markov processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}